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<article class="li"><h3 class="heading">
<span class="type">Item</span><span class="space"> </span><span class="codenumber">2.e</span><span class="period">.</span>
</h3>
<p>You can find <span class="process-math">\(y(t)\)</span> by differentiating and substituting <span class="process-math">\(\frac{dx}{dt}\)</span> in either of the system equations. Quicker here is to subtract the second equation from the first to obtain</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
-2\frac{dx}{dt}+y+x+2x=e^t-e^{2t}
\end{equation*}
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<p class="continuation">so</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y(t)=2\frac{dx}{dt}-3x+e^t-e^{2t}.
\end{equation*}
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